1. Reflectivity Measurements of Oxide Layers on Glass
In this presentation the use of a Philips X’Pert PRO MRD for reflectivity measurements on glass samples with oxide layers is demonstrated.
Note to the presenter: The complete story of this presentation is described in the Philips Analytical Application Note “Reflectivity Measurements of Oxidic Layers on Glass Surfaces” ( )

2. Reflectivity Measurements of Oxide Layers on Glass
Contents:
Applications
Principle
Instrumentation
Evaluation
Examples
Conclusions
After a short introduction into the possible application areas for reflectivity measurements, the method and a possible reflectivity set-up in a Philips X’Pert PRO MRD is shown
The evaluation of the layer parameters from a measurement are described.
Afterwards the possibilities to characterize thin layers by X-ray reflectivity are demonstrated by 4 examples of oxide layers on glass.
The presentation will end with a summary.

3. Applications X-ray reflectivity : Measurement to determine
Layer thickness ( %)
Density ( 1 - 2%)
Interface roughness, etc. of
Glass coatings
Semiconductors
Magnetic or optical media, etc.
In new technologies thin layered materials become increasingly important. Single or complex multi-layer structures can be found in all kinds of research and development areas, like semiconductors, magnetic multi-layers, various types of coatings and optical applications. Thus there is an increasing interest in precise characterization methods for these layers. Some important parameters of these layers can be determined by X-ray reflectometry.
X-ray reflectivity allows the measurement of parameters like layer thickness, interface roughness and layer density. The thickness of a layer can be determined with an accuracy of up to  % (range: from a few nanometers up to few hundred nanometers) and the density with an accuracy of  1 - 2%. The accuracy of the interface roughness that can be derived from the measurement (as well as the absolute values) depends on the roughness model that is used.
(The layers can be single crystalline, polycrystalline or amorphous.)
Herewith X-ray reflectivity allows the description of thin films. It also allows to analyse and to control development and production processes.

4. Principle (1) Below c beam penetrates only few nm
Above c penetration depth increases sharply
n1= 1  n2 d n3
 2
This figure illustrates the principle of the measurements.
Far below the critical angle of total external reflection X-rays penetrate only a few nanometers (typically nm) into condensed matter. Above the critical angle the penetration depth increases rapidly.
The critical angle c is related to the density of the layer.
According to Snellius’ law, the critical angle c at a surface (refractive index n) in vacuum (refractive index n = 1) is given by:
cos c = n
For small values of c this formula can be approximated by
1 - ½ (c) 2 = n
With n = 1 -  + i,  the dispersive correction and  the absorption correction and neglecting the absorption, it can be shown that the critical angle c (in radians) is proportional to the square root of .  is related to the electron density. Therefore in general the determination of the critical angle c gives the electron density and, with known stochiometric composition, the mass density of the reflecting medium.

5. Principle (2) Permits surface/layer analysis
Partial reflection at each layer interface
Interference of reflected beams creates oscillations in reflectivity curves
n1= 1  n2 d n3
 2
At every interface where the electron density changes, a part of the X-ray beam is reflected. The interference of these partly reflected X-ray beams creates the oscillations shown in reflectivity measurements.
Therefore Grazing Incidence X-ray Reflectivity (GIXR) can be used to analyse sample surfaces and thin layers.
Permits surface/layer analysis

6. Principle (3) Grazing incidence X-ray reflectivity (GIXR):
Oxide layers on glass
Grazing incidence X-ray reflectivity (GIXR):
Sample reflectivity measured around critical angle of total reflection c
Measurement over 4 - 5º  range, 7+orders of reflectivity magnitude
Coupled q-2q scan
In a GIXR measurement the reflectivity of the sample is measured around the critical angle of total reflection.
Provided the reflectivity is measured over a “wide” angular range ( approx o) and over at least seven orders of magnitude in reflectivity, a minimum layer thickness in the order of 1 nm can be proven under optimal sample conditions (see examples). The method is sufficiently sensitive to provide precise information on the presence of interface layers in layered structures.
The reflectivity measurements are performed as coupled -2 - scans.

7. Principle (4)
This graph shows schematically a typical reflectivity measurement and the information contained. The shape of the graph at total reflection - i.e. the “plateau” below the critical angle - is determined by the size of the sample, its flatness and by instrumental parameters (e.g. beam size).
The critical angle is determined by the electron density (of the top layer) and, with known stochiometric composition, the mass density of the reflecting medium can be derived. The oscillations are created by the interference of partially reflected X-ray beams from different depths within the sample corresponding to changes in the electron density. These changes are present at layer interfaces and at the top surface of a coating.
The spacing of the oscillations gives information about the different layer thicknesses. In addition the general shape of the curve as well as the amplitudes of the oscillations correspond to surface and interface roughnesses, density fluctuations and the resolution of the instrument.
Note: The shown “modulation” of the oscillations (as shown in the graph) appear in multi-layer measurements (different thicknesses.).

8. Instrumentation (1) Philips X’Pert PRO Materials Research
Oxide layers on glass
Philips
X’Pert PRO
Materials
Research
Diffractometer
Here a typical experimental set-up used for reflectivity measurements in a Philips X’Pert PRO Materials Research Diffractometer (MRD) is shown. The openings of the anti-scatter slit and the receiving slit are used in a coupled mode: the so-called beam tunnel mode.
The X’Pert PRO Diffractometer allows a highly accurate adjustment of the sample with respect to the incident beam and - using an automatic attenuator - the measurement of a large dynamic intensity range.
Both instrumental aspects are most important for reflectivity measurements:
The measurement of a reflectivity curve is performed using a coupled -2 scan.

9. Instrumentation (2) X-ray tube Cu anode, LFF, 40 kV/40 mA
PDS beam width <0.04º 2
Alignment accuracy ± º (in w)
Attenuator automatic at high intensities
PRS/PASS coupled (50-100mm)
Monochromator graphite
Soller slits 0.04 rad
The used X-ray source in the application examples is a sealed tube with copper anode and long-fine focus of optical height 40 m. The experiments presented have been performed with a generator setting of 40 kV / 40 mA.
The programmable divergence slit (PDS) at the incident beam side has been set to provide a small opening corresponding to a beam width of less than 0.04o in 2.
This allows for an accurate calibration of the 2 zero position (direct beam) and an accurate adjustment of the sample with respect to the incident beam. The alignment should be done with an accuracy of approx o in order to determine the critical angle c within a few thousands of a degree.
In order to extend the dynamic range of the detector an incident beam attenuator is automatically inserted at high intensities. This increases the dynamic intensity range to decades.
On the diffracted beam side a programmable receiving slit (PRS) and a programmable anti-scatter slit (PASS) are used. In the measurements the PRS and PASS are used in a coupled mode - the so-called beam tunnel mode: both have the same fixed opening of m (electronically controlled).
An additional monochromator in front of the detector limits the detected wavelength range. Soller slits (0.04 rad) on both (the incident and the diffracted) sides limit the axial divergence.

10. Evaluation GIXA software simulates and fits experimental data
Oxide layers on glass
GIXA software simulates and fits experimental data
User inputs estimates of instrumental resolution, sample parameters
Calculate simulated curve, compare with collected data
Manual/automatic fit
The information from the experimental data is extracted with the Philips Gixa software. This program can be used to simulate and fit experimental reflectivity data.
It requires the user to input estimates about the instrumental resolution as well as sample parameters. Estimates about the film coating (number of layers), layer thicknesses, interface roughnesses and information about compositions and densities are used as a starting point for the simulation.
The estimated parameters are used to calculate a simulated reflectivity curve which is then graphically compared with the collected data.
The simulation process can be continued by either manually changing the sample parameters or by an automated fit process, which uses the simplex-algorithm and simulated thermal annealing methods.

11. Application examples Measurement of oxide layers on glass surfaces
to monitor changes in glass melt and
surface corrosion during production
Acknowledgement: Dr. O. Anderson, SCHOTT GLAS, Germany
The following examples shall demonstrate the characterization of oxide layers on glass surfaces.
In this application area e.g. changes in glass melt during production and the corrosion of glass surfaces can be determined. This allows to control the cleaning and polishing processes of glass surfaces.
I would like to thank Dr. O. Anderson from SCHOTT GLAS in Germany for placing the measurement results at our disposal.

12. Example 1: Polished BK7 borosilicate glass
Reflectivity recorded over 7 orders of magnitude
Excellent fit agreement
Thin layers are determinable
This figure shows the collected reflectivity data as well as the simulated curve for a polished BK7 glass sample (borosilicate glass). The reflectivity has been recorded over 7 orders of magnitude in intensity.
The graph shows the excellent agreement between simulation and experiment in the region of total reflection and near the critical angle. The high precision in the detection of density changes and absolute density values requires a good sample quality, an accurate adjustment of the sample and a good fit in the region around the critical angle.
The collected data can only be fitted by the assumption of a thin leached layer of 2.4 nm on the glass surface. These layers of lower density (  2.0 g/cm3 - c approx o)- compared to the bulk glass ( = 2.52 g/cm3) - originate during the cleaning process of the glass.
(Note: The fit values for the roughnesses are  = 1.0 nm for the leached layer and  = 1.5 nm for the substrate. These comparably high roughnesses indicate the presence of a graded layer.)
This example shows that even thin layers of only few nanometer thickness can be detected by X-ray reflectometry.

13. Example 2: Ion plated (IP) and reactive evaporated (RE) TiO2 on glass
Density: IP > RE
Roughness: RE > IP
This figure shows the comparison of measurement curves of ion plated (IP) as well as reactive evaporated (RE) TiO2 layers on borosilicate glass (BK7). The data clearly demonstrate that ion plated TiO2 layers have a much higher density than TiO2 layers produced by reactive evaporation (as can be seen from the measured critical angles).
(c (RE) = 0.26o / c (IP) = 0.28o - resolution approx o)
The simulation for the two different samples yields layer densities of  = 3.8 g/cm3 for the ion plated TiO2 layer and  = 3.1 g/cm3 for the reactive evaporated TiO2 layer.
In addition the higher surface roughness of the RE layer compared to the IP layer becomes visible in the shape of the curve, because of sharper decrease in intensity.

14. Example 3: Coated float glass (1)
Good visibility
of oscillations
up to
high angles
7 decades
dynamic range
The graph shows a measurement on float glass coated with Ta.
This example demonstrates that with the experimental set-up described above excellent measurements up to high angles (2 up to 10o ) with a high dynamic range (7 decades) are possible.
The graph shows clearly the presence of inter-layers (amplitude modulation of the oscillations).
This measurement could excellently be fitted by assuming a multi-layer system Ta-oxide / Ta / Ta-oxide / float glass.
From the fit it could be concluded that the Ta-oxide layers have a thickness of 2 and 3 nm respectively.
The fit delivered:
Thickness Density Roughness
Ta-oxide 3 nm 7.0 g/cm3 0.3 nm
Ta 23.5 nm 14.5 g/cm3 0.4 nm
Ta-oxide 2 nm 8.5 g/cm3 0.3 nm
float glass 2.5 g/cm3 0.4 nm

15. Example 3: Coated float glass (2)
High 2 measurements -> 10º over 7 decades dynamic range possible
Good visibility of oscillations up to high angles requires interface roughness < 3-4 Å
High quality measurement allows fit of complex multi-layer structures
For good visible oscillations at high 2 angles low interface roughness of less than 3-4  are necessary.
These circumstances are necessary for the simulation of complex multi-layer structures. They allow to collect all important experimental data for a perfect simulation.

16. Example 4: Multi-layer coated soda-lime glass
(anti-reflection coating)
On this slide the collected and simulated data of a multi-layer system consisting of a SiO2 layer, a TiO2 layer and a layer of SiO2/TiO2 on soda-lime glass are shown. Such multi-layer systems are used as an anti-reflection coating.
Even this complex multi-layer system can be fitted with good agreement to the experimental data.

17. Example 4 Fit requires good knowledge of approximate parameters
Good fit quality visible in fine structure of oscillations
For such complex multi-layer structures a good knowledge of the approximate parameters of the sample is required to reach good fit results within an acceptable time. For the evaluation of the measurement knowledge of the order of the layers is necessary.
The simulation allows also a good fit of the fine structure of the oscillations (graph on right side) indicating a good quality of the fit. Remaining differences might be due to inhomogeneities in the layers and density gradients at the interface of the layers.

18. Conclusion
X-ray reflectivity is a powerful technique for measuring parameters of thin layers
High quality data can be recorded with the X’Pert PRO X-ray diffraction system
(Large dynamic range / up to high 2-angles)
Even thin layers and interface layers are determinable
Allows fit of complex multi-layer structures
X-ray reflectivity performed on a Philips X’Pert PRO Materials Research Diffractometer offers a powerful non-destructive tool to characterise thin layers. In combination with the GIXA software it provides a fast method to extract sample parameters with high accuracy.
The examples show that with the described experimental set-up high quality data can be recorded. Measurements up to high 2-angles are possible and the reflectivity can be recorded over a large dynamic range.
This allows the determination of even thin layers, gives information about originated interface layers and provides the possibility to measure and analyze complex multi-layer structures.
Reflectivity can be used for analysis as well as for control and optimisation of development and production processes.